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Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a sour...
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stre...
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines)...
Advanced Fluid Mechanics Determine the streamfunction and velocity potential for uniform flow of strength U over a p...
Advanced Fluid Mechanics
Determine the streamfunction and velocity potential for uniform flow of strength U over a point source and sink of equal strength, m, located on the x-axis at +/-b (the source is at-b with the sink at +b, where b is not small). Write expressions for the u and v velocity components, and draw streamlines of the flow. Determine the location(s) of any and all stagnation points.
Determine the streamfunction and velocity potential for uniform flow of strength...
a) Derive the general stream function of a potential flow around a cylinder of radius R given the stream functions Y of a uniform flow and a doublet are uniformUy 'doublet where Uis the speed of...
a) Derive the general stream function of a potential flow around a cylinder of radius R given the stream functions Y of a uniform flow and a doublet are uniformUy 'doublet where Uis the speed of the uniform flow and C is the strength of the doublet. (5 marks) b) Find the specific stream function assuming the streamline on the surface of the cylinder is Ψ-0 (5 marks) c) Find the velocities at two points (-3R, 0 and (-2R, 0)....
Question 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfi...
Question 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfield around a cylinder. The resulting velocity potential for the flow is given by: A cos Ur cos e The resulting velocity field in cylindrical coordinates is given by - = 4 r ae ar where e, and eo are the unit vectors in cylindrical polar coordinates, Uo is the free-stream velocity and A an arbitrary parameter. a) (10 points) Determine...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coo...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coordinates, the stream function can be written as ψ Uosine (r-7/-Kln (5). where R is the radius of the cylinder. Assuming that the pressure in the far upstream is po. find the pressure distribution on the surface.
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1....
Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1...
Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1 m/s, B = 1 s−1, and the coordinates are measured in meters. Obtain expressions forthe velocity field and the stream function. Using water as the working fluid, calculate the pressure difference between the origin and the point (x,y) = (1,2). What is the volume flow rate (per unit depth) between streamlines passing through these two points?
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y...
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
3. (4 pts) Write down the velocity potential for a lifting circular cylinder in a uniform...
3. (4 pts) Write down the velocity potential for a lifting circular cylinder in a uniform flow of velocity V. Find the velocity components in this flow field. For what value of the circulation will the stagnation point be located on the surface of the cylinder at: (a) (r, 8) = (RO), (b) (r,®) = (R, -*/2).
6.102 The flow field for a plane source at a distance h above an infinite wall...
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
Name: Problem 4 (20 pts). The velocity potential for a cylinder rotating in a uniform stream of fluid is 2TT where U, a, Г are constants. The density of the flow is , and gravitational force is n...
Name: Problem 4 (20 pts). The velocity potential for a cylinder rotating in a uniform stream of fluid is 2TT where U, a, Г are constants. The density of the flow is , and gravitational force is negligible. Compute the pressure difference between points A and B. -+
Name: Problem 4 (20 pts). The velocity potential for a cylinder rotating in a uniform stream of fluid is 2TT where U, a, Г are constants. The density of the flow is...
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines)...
Advanced Fluid Mechanics
Determine the streamfunction and velocity potential for uniform flow of strength U over a point source and sink of equal strength, m, located on the x-axis at +/-b (the source is at-b with the sink at +b, where b is not small). Write expressions for the u and v velocity components, and draw streamlines of the flow. Determine the location(s) of any and all stagnation points.
Determine the streamfunction and velocity potential for uniform flow of strength...
a) Derive the general stream function of a potential flow around a cylinder of radius R given the stream functions Y of a uniform flow and a doublet are uniformUy 'doublet where Uis the speed of the uniform flow and C is the strength of the doublet. (5 marks) b) Find the specific stream function assuming the streamline on the surface of the cylinder is Ψ-0 (5 marks) c) Find the velocities at two points (-3R, 0 and (-2R, 0)....
Question 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfield around a cylinder. The resulting velocity potential for the flow is given by: A cos Ur cos e The resulting velocity field in cylindrical coordinates is given by - = 4 r ae ar where e, and eo are the unit vectors in cylindrical polar coordinates, Uo is the free-stream velocity and A an arbitrary parameter. a) (10 points) Determine...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coordinates, the stream function can be written as ψ Uosine (r-7/-Kln (5). where R is the radius of the cylinder. Assuming that the pressure in the far upstream is po. find the pressure distribution on the surface.
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1....
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
3. (4 pts) Write down the velocity potential for a lifting circular cylinder in a uniform flow of velocity V. Find the velocity components in this flow field. For what value of the circulation will the stagnation point be located on the surface of the cylinder at: (a) (r, 8) = (RO), (b) (r,®) = (R, -*/2).
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
Name: Problem 4 (20 pts). The velocity potential for a cylinder rotating in a uniform stream of fluid is 2TT where U, a, Г are constants. The density of the flow is , and gravitational force is negligible. Compute the pressure difference between points A and B. -+
Name: Problem 4 (20 pts). The velocity potential for a cylinder rotating in a uniform stream of fluid is 2TT where U, a, Г are constants. The density of the flow is...
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